Question

Calcule f''(x), sendo f(x)= ㏑(3x²-4)

Answer 1

$\mathsf{f(x)=\ell\,n(3x^2-4)}\\\mathsf{f'(x)=\dfrac{6x}{3x^2-4}}$

$\mathsf{f''(x)=\dfrac{6(3x^2-4)-6x(6x)}{(3x^2-4)^2}}\\\mathsf{f''(x)=\dfrac{18x^2-24-36x^2}{(3x^2-4)^2}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{f''(x)=-\dfrac{18x^2+24}{(3x^2-4)^2}}}}}}$